With two seven inning games already in the books, our dauntless editor asked me to estimate the chances of a no-hitter in a seven inning game. I can give a first-cut at that, but there are a lot of caveats.
First off, using the Retrosheet database (1921-2019) I can look at all 328,844 starting pitcher performances. I can then see how many had given up no hits conditional on having reached a particular inning. When we do this, we get the following table:
The first interesting thing to notice about this table is that each row is pretty close to half the row above it. The first and fourth innings have some more attrition than that, which is unsurprising since the pitcher is facing the best hitters of the opposition, assuming no more than a few walks or other base runners with no hits.
Note that this table takes no account of multi-pitcher no hitters, nor does it ensure that the pitcher actually finished whatever inning he reached, so if a pitcher is removed with one out in the seventh having not yielded a hit I will still credit them as hitless through 7. It also takes no account of the DH, which clearly reduces the probability of no-hitters.
Finally, there is no adjustment for no-hitter pressure or managerial strategy to break up a no-hitter. Presumably going through the seventh without a hit is somewhat more pressured in a seven inning game than in a nine inning game, though the fact that the 9th is actually more than half the 8th suggests that this effect can’t be very large, since the 9th would, under this theory, be more difficult than the 8th. It doesn’t appear to be.
With those caveats in mind, we see that there are 4.5 times more no-hitters through 7 than through 9. So a no-hitter probability of about 6 per 10,000 nine-inning games rises to 27 per 10,000 seven-inning games.
A table of great Braves pitching performances that ends with Folty and Newk just makes you sad. But getting back to the point at hand, he Braves are pretty much in line with the statistics here. They have 2 no-hitters and 20 no-hitters through 7, so they have been ten times more likely to have a no-hitter through 7 innings as one through 9. (Of course, if you throw in the Mercker/Wohlers/Pena no-hitter of 9/11/91, the the ratio drops to 7-1.)